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MATA20H3 Calculus A
Limits, continuity, derivatives, derivatives of higher order, analysis of graphs, use of derivatives, integrals and their applications, fundamental theorem of Calculus.
Exclusion: (MATA27H), MATA30H , MATA32H , MAT123H, MAT124H, MAT125H, MAT126H, MAT133Y, MAT135Y, MAT137Y, MAT157Y, JMB170Y
Prerequisite: Grade 12 Advanced Functions
MATA21H3 Calculus B
Techniques of integration, sequences, series, Taylor series, differential equations.
Exclusion: (MATA27H), MATA30H , MATA32H , MATA33H , MATA35H , MATA36H , MATA37H , MAT123H, MAT124H, MAT125H, MAT126H, MAT133Y, MAT135Y, MAT137Y, MAT157Y, JMB170Y
Prerequisite: MATA20H
MATA23H3 Linear Algebra I
Systems of linear equations, matrices, Gaussian elimination; vector spaces, basis, dimension; inner product spaces, geometry in R^n; linear transformations; determinants, Cramer's rule; eigenvalues and eigenvectors, diagonalization; orthogonal transformations.
Exclusion: MAT223H
Prerequisite: Grade 12 Vectors and Calculus or [Grade 12 Advanced Functions and Introductory Calculus & Geometry and Discrete Mathematics]
MATA30H3 Calculus I
An introduction to the basic techniques of Calculus. Elementary functions: rational, trigonometric, root, exponential and logarithmic functions and their graphs. Basic calculus: limits, continuity, derivatives, derivatives of higher order, analysis of graphs, use of derivatives; integrals and their applications, techniques of integration.
Exclusion: MATA20H , MATA32H , MAT123H, MAT124H, MAT125H, MAT126H, MAT133Y, MAT135Y, MAT137Y, MAT157Y, JMB170Y, (MATA27H)
Prerequisite: Grade 12 Vectors and Calculus
MATA32H3 Calculus for Management I
This is a calculus course with most examples and applications of an economic nature. Topics to be covered: linear programming (geometric); introduction to financial mathematics; continuous functions including exponential and logarithmic functions with applications to finance; differential calculus of one variable; marginal analysis; optimization of single variable functions; techniques of integration.
Exclusion: MATA20H , (MATA27H), MATA30H , MAT123H, MAT125H, MAT133Y, MAT135Y, MAT136Y, MAT137Y, MAT157Y, JMB170Y
Prerequisite: Grade 12 Vectors and Calculus.
MATA33H3 Calculus for Management II
This course will introduce the students to multivariable calculus and linear algebra. Topics will include: matrix algebra; multi-variable functions; contour maps; partial and total differentiation; optimization of multi-variable functions; optimization of constrained multi-variable functions; Lagrange multipliers.
Exclusion: MATA21H , (MATA27H), MATA35H , MATA36H , MATA37H , MAT124H, MAT126H, MAT133Y, MAT134Y, MAT135Y, MAT136Y, MAT137Y, MAT157Y, JMB170Y
Prerequisite: MATA32H
MATA35H3 Calculus II for Biological Sciences
A calculus course emphasizing examples and applications in the biological and environmental sciences. Discrete probability; basic statistics: hypothesis testing, distribution analysis. Basic calculus: extrema, growth rates, diffusion rates; differential equations; population dynamics; vectors and matrices in 2 and 3 dimensions; genetics applications.
Note: This course will not satisfy the Mathematics requirements for any Program in Computer and Mathematical Sciences, nor will it normally serve as a prerequisite for further courses in Mathematics. Students who are not sure which Calculus II course they should choose are encouraged to consult with the supervisor(s) of Programs in their area(s) of interest.
Exclusion: MATA21H , MATA33H , MATA36H , MATA37H , MAT123H, MAT124H, MAT125H, MAT126H, MAT133Y, MAT135Y, MAT137Y, MAT157Y, JMB170Y, (MATA27H)
Prerequisite: MATA30H
MATA36H3 Calculus II for Physical Sciences
This course is intended to prepare students for the physical sciences. Topics to be covered include: Newton's method, approximation of functions by Taylor polynomials, numerical methods of integration, complex numbers, sequences, series, Taylor series, differential equations.
Exclusion: MATA21H , MATA33H , MATA35H , MATA37H , MAT123H, MAT124H, MAT125H, MAT126H, MAT133Y, MAT135Y, MAT137Y, MAT157Y, JMB170Y
Prerequisite: MATA30H
MATA37H3 Calculus II for Mathematical Sciences
A calculus course providing a conceptual approach for students needing more than techniques and applications. An introduction to proof and the theoretical side of basic calculus emphasizing intuition. Fundamental Theorem of Calculus, Taylor's Theorem, sequences and series, power series and differential equations.
Exclusion: MATA21H , MATA33H , MATA35H , MATA36H , MAT123H, MAT124H, MAT125H, MAT126H, MAT133H, MAT135H, MAT137H, MAT157Y, JMB170Y
Prerequisite: MATA30H
MATB24H3 Linear Algebra II
Fields, vector spaces over a field, linear transformations; diagonalizability, invariant subspaces, Cayley-Hamilton theorem; hermitian inner product, normal, self-adjoint and unitary operators, method of least squares, introduction to coding theory.
Exclusion: MAT224H
Prerequisite: MATA23H or MAT223H
MATB41H3 Techniques of the Calculus of Several Variables I
Partial derivatives, gradient, tangent plane, Jacobian matrix and chain rule, Taylor series; extremal problems, extremal problems with constraints and Lagrange multipliers, multiple integrals, spherical and cylindrical coordinates, law of transformation of variables.
Exclusion: MAT232H, MAT235Y, MAT237Y, MAT257Y
Prerequisite: [MATA23H or MAT223H] & [[MATA36H or MATA37H ] or MAT137Y or MAT157Y]]
MATB42H3 Techniques of the Calculus of Several Variables II
Fourier series. Vector fields in R^n, Divergence and curl, curves, parametric representation of curves, path and line integrals, surfaces, parametric representations of surfaces, surface integrals. Green's, Gauss', and Stokes' theorems will also be covered. An introduction to differential forms, total derivative.
Exclusion: MAT235Y, MAT237Y, MAT257Y, MAT368H
Prerequisite: MATB41H
MATB43H3 Introduction to Analysis
Calculus revisited rigorously: properties of real numbers, limits, compactness, topology of Euclidean space, continuity, differentiability, fundamental theorem, Riemann integral.
Exclusion: MAT246Y
Prerequisite: [MATA37H or MAT137Y] & MATB24H
Corequisite: MATB42H
MATB44H3 Differential Equations I
Ordinary differential equations of the first and second order, existence and uniqueness; solutions by series and integrals; linear systems of first order; non-linear equations; difference equations.
Exclusion: MAT244H, MAT267H
Prerequisite: [MATA36H or MATA37H ] & MATA23H
Corequisite: MATB41H & MATB24H
MATB61H3 Linear Programming and Optimization
Linear programming, simplex algorithm, duality theory, interior point method; quadratic and convex optimization, stochastic programming; applications to portfolio optimization and operations research.
Exclusion: APM236H
Prerequisite: MATA23H
Corequisite: MATB42H
MATC01H3 Groups and Symmetry
Congruences and fields. Permutations and permutation groups. Linear groups. Abstract groups, homomorphisms, subgroups. Symmetry groups of regular polygons and Platonic solids, wallpaper groups. Group actions, class formula. Cosets, Lagrange's theorem. Normal subgroups, quotient groups. Emphasis on examples and calculations.
Exclusion: MAT301H, MAT347Y
Prerequisite: MATA37H & [MATB24H or MAT224H]
MATC02H3 Fields and Groups
Abstract group theory: Sylow theorems, groups of small order, simple groups, classification of finite abelian groups. Fields and Galois theory: polynomials over a field, field extensions, constructibility; Galois groups of polynomials, in particular cubics; insolvability of quintics by radicals.
Exclusion: (MAT302H), MAT347Y
Prerequisite: MATC01H
MATC09H3 Introduction to Mathematical Logic
Predicate calculus. Relationship between truth and provability; Gödel's completeness theorem. First order arithmetic as an example of a first-order system. Gödel's incompleteness theorem; outline of its proof. Introduction to recursive functions.
Exclusion: MAT309H, CSC438H
Prerequisite: MATB24H & [MATB43H or CSCB36H ]
MATC15H3 Introduction to Number Theory
Elementary topics in number theory; arithmetic functions; polynomials over the residue classes modulo m, characters on the residue classes modulo m; quadratic reciprocity law, representation of numbers as sums of squares.
Exclusion: MAT315H
Prerequisite: [MATA36H or MATA37H ] & MATB24H
MATC16H3 Coding Theory and Cryptography
The main problems of coding theory and cryptography are defined. Classic linear and non-linear codes. Error correcting and decoding properties. Cryptanalysis of classical ciphers from substitution to DES and various public key systems [e.g. RSA] and discrete logarithm based systems. Needed mathematical results from number theory, finite fields, and complexity theory are stated.
Prerequisite: MATB24H & STAB52H
Corequisite: MATC15H recommended
MATC25H3 Classical Plane Geometries and their Transformations
An introduction to geometry with a selection of topics from the following: symmetry and symmetry groups, finite geometries and applications, non-Euclidean geometry.
Exclusion: MAT402H, (MAT365H)
Prerequisite: MATA23H
Corequisite: MATC01H
MATC27H3 Introduction to Topology
Fundamentals of set theory, topological spaces and continuous functions, connectedness, compactness, countability, separatability, metric spaces and normed spaces, function spaces, completeness, homotopy.
Exclusion: MAT327H
Prerequisite: MATB24H & MATB43H
MATC32H3 Graph Theory and Algorithms for its Applications
Graphs, subgraphs, isomorphism, trees, connectivity, Euler and Hamiltonian properties, matchings, vertex and edge colourings, planarity, network flows and strongly regular graphs; applications to such problems as timetabling, personnel assignment, tank form scheduling, traveling salesmen, tournament scheduling, experimental design and finite geometries.
Prerequisite: [MATB24H or CSCB36H ] & at least one other B-level course in Mathematics or Computer Science
MATC34H3 Complex Variables
Theory of functions of one complex variable, analytic and meromorphic functions. Cauchy's theorem, residue calculus, conformal mappings, introduction to analytic continuation and harmonic functions.
Exclusion: MAT334H
Prerequisite: MATB42H
MATC35H3 Chaos, Fractals and Dynamics
Topics covered include: metric spaces, dynamics on the real line, fixed points, periodic points, attractors, repellers, Sharkovski's theorem parametrized families of functions and bifurcations, period doubling, dynamics of the logistic map, symbolic dynamics, chaos, topological equivalence of the logistic map and the shift map, Newton's method; dynamics on the complex line, iterations of rational functions, Julia sets, Mandelbrot set.
Exclusion: MAT335H
Prerequisite: MATB43H
MATC37H3 Introduction to Real Analysis
Metric spaces, completeness, uniform convergence. Topics in measure theory: the Lebesgue integral, Riemann-Stieltjes integral, Lp spaces, Fourier series.
Exclusion: MAT337H, (MATC38H)
Prerequisite: MATB43H
MATC44H3 Introduction to Combinatorics
Basic counting principles, generating functions, permutations with restrictions. Fundamentals of graph theory with algorithms; applications (including network flows). Combinatorial structures including block designs and finite geometries.
Exclusion: MAT344H
Prerequisite: MATB24H
MATC46H3 Differential Equations II
Sturm-Liouville problems, Green's functions, special functions (Bessel, Legendre), partial differential equations of second order, separation of variables, integral equations, Fourier transform, stationary phase method.
Exclusion: APM346H
Prerequisite: MATB44H & MATB24H
Corequisite: MATB42H
MATC58H3 An Introduction to Mathematical Biology
Mathematical analysis of problems associated with biology, including models of population growth, cell biology, molecular evolution, infectious diseases, and other biological and medical disciplines. A review of mathematical topics: linear algebra (matrices, eigenvalues and eigenvectors), properties of ordinary differential equations and difference equations.
Prerequisite: MATB44H
MATC63H3 Differential Geometry
Curves and surfaces in Euclidean 3-space. Serret-Frenet frames and the associated equations, the first and second fundamental forms and their integrability conditions, intrinsic geometry and parallelism, the Gauss-Bonnet theorem.
Exclusion: MAT363H
Prerequisite: MATB43H
MATC65H3 Complex Variables II
Applications of complex analysis to geometry, physics and number theory. Fractional linear transformations and the Lorentz group. Solution to the Dirichlet problem by conformal mapping and the Poisson kernel. The Riemann mapping theorem. The prime number theorem.
Exclusion: MAT354H
Prerequisite: MATC34H
MATC82H3 Mathematics for Teachers
The course discusses the Mathematics curriculum (K-12) from the following aspects: the strands of the curriculum and their place in the world of Mathematics, the nature of proofs, the applications of Mathematics, and its connection to other subjects.
Exclusion: MAT382H
Prerequisite: [MATA23H & MATA37H ] or [MATA23H & MATA36H & [CSCA65H or MATB24H ]]
MATC90H3 Beginnings of Mathematics
Mathematical problems which have arisen repeatedly in different cultures, e.g. solution of quadratic equations, Pythagorean theorem; transmission of mathematics between civilizations; high points of ancient mathematics, e.g. study of incommensurability in Greece, Pell's equation in India.
Exclusion: MAT390H
Prerequisite: One Grade 12 Mathematics course & 5.0 full university courses
MATD12H3 Topics in Mathematics
A variety of topics from geometry, analysis, combinatorics, number theory and algebra, to be chosen by the instructor
Prerequisite: MATC01H & [MATC35H or MATC37H ] & [MATC15H or (MATD02H)]
MATD61H3 Introduction to Industrial Mathematics
Monte Carlo Method (mean time between failures, servicing requests), Data Manipulation (z-transform, filters, Bode Plots), Discrete Fourier Transform (real time processing , FFT, image processing), Regression (best fit to discrete data, Hilbert Space, Gram's theorem), Frequency-Domain Methods, Numerical Models for PDE, Galerkin's methods, Cubic Splines.
The course provides extensions of mathematics useful in industrial problems, interweaving analytic and computing methods during problem solving.
Prerequisite: MATB42H & MATB44H & STAB52H
Recommended preparation: MATB61H & MATC46H
MATD95H3 Readings in Mathematics
Independent study under direction of a faculty member.
Prerequisite: MATC01H & [MATC35H or MATC37H ] & [MATC15H or (MATD02H)]
SCIB01H3 Science Engagement Outreach
SCIB02H3 Science Engagement In-Reach
(See the Science Engagement section of this Calendar for full course descriptions.)
Published Wednesday July 23rd, 2008 Section last updated Wed Jul 16, 2008
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Calendar 2008-2009 Back to Management Continue to Neuroscience Up to Table of Contents and Search or Alphabetic Index |